Exhibit 1.1

HYPERION DEFI, INC.

Shares of Common Stock

($0.0001 par value per share)

AMENDMENT NO. 1 TO

AMENDED AND RESTATED SALES AGREEMENT

September 24, 2025

CHARDAN CAPITAL MARKETS, LLC

One Pennsylvania Avenue, Suite 4800

New York, New York 10119

Ladies and Gentlemen:

Reference is made to the Amended and Restated Sales Agreement, dated December 30, 2024 (the “Agreement”), by and between Hyperion DeFi, Inc. (f/k/a Eyenovia, Inc.), a Delaware corporation (the “Company”), and Chardan Capital Markets, LLC (the “Agent”). The Company and the Agent (collectively, the “Parties”) wish to amend the Agreement, pursuant to Section 15 of the Agreement, to increase the aggregate offering price under the Agreement (this “Amendment”). The Parties therefore hereby agree as follows:

1.                  On the date hereof, the Company has filed or will file a Prospectus Supplement relating to the offering of up to $60,225,987 of Common Stock (the “September 2025 ATM Prospectus Supplement”), to the base prospectus, dated October 8, 2024, contained in the registration statement on Form S-3 (Registration No. 333-282458). The September 2025 ATM Prospectus Supplement shall update and amend the prospectus supplement filed by the Company on October 1, 2024, as supplemented by the prospectus supplements filed on the Company on December 30, 2024, April 17, 2025, June 2, 2025, June 27, 2025 and July 7, 2025, relating to the Common Stock offered pursuant to the Agreement in its entirety.

2.                   Issuance and Sale of Shares. Section 1 of the Agreement is hereby amended and restated in its entirety to read as follows:

“The Company agrees that, from time to time during the term of this Agreement, on the terms and subject to the conditions set forth herein, it may issue and sell through the Agent up to $100.0 million of shares of common stock, $0.0001 par value per share, of the Company (the “Common Stock”), subject to the limitations set forth in Section 5(c) (the “Placement Shares”). Notwithstanding anything to the contrary contained herein, the parties hereto agree that compliance with the limitation set forth in this Section 1 on the aggregate gross sales price of Placement Shares that may be issued and sold under this Agreement from time to time shall be the sole responsibility of the Company, and that the Agent shall have no obligation in connection with such compliance. The issuance and sale of Placement Shares through the Agent will be effected pursuant to the Registration Statement (as defined below) filed by the Company and declared effective by the Securities and Exchange Commission (the “Commission”) , although nothing in this Agreement shall be construed as requiring the Company to issue any Placement Shares.

The Company has filed or will file, in accordance with the provisions of the Securities Act of 1933, as amended, and the rules and regulations thereunder (collectively, the “Securities Act”), with the Commission a registration statement on Form S-3, including a base prospectus, relating to certain securities, including the Common Stock, to be issued from time to time by the Company, and which incorporates by reference documents that the Company has filed or will file in accordance with the provisions of the Securities Exchange Act of 1934, as amended, and the rules and regulations thereunder (collectively, the “Exchange Act”). The Company has prepared a prospectus supplement to the base prospectus included as part of such registration statement, which prospectus supplement specifically relates to the Placement Shares to be issued from time to time pursuant to this Agreement (“Prospectus Supplement”). The Company will furnish to the Agent, for use by the Agent, copies of the base prospectus included as part of such registration statement at the time it became, as supplemented by the Prospectus Supplement. Except where the context otherwise requires, such registration statement, including all documents filed as part thereof or incorporated by reference therein, and including any information contained in a Prospectus (as defined below) subsequently filed with the Commission pursuant to Rule 424(b) under the Securities Act or deemed to be a part of such registration statement pursuant to Rule 430B or Rule 462(b) under the Securities Act, is herein called the “Registration Statement.” The base prospectus, including all documents incorporated therein by reference, included in the Registration Statement, as it may be supplemented by the Prospectus Supplement, in the form in which such prospectus and/or Prospectus Supplement have most recently been filed by the Company with the Commission pursuant to Rule 424(b) under the Securities Act, together with any “issuer free writing prospectus” (as used herein, as defined in Rule 433 under the Securities Act (“Rule 433”)), relating to the Placement Shares that (i) is required to be filed with the Commission by the Company or (ii) is exempt from filing pursuant to Rule 433(d)(5)(i), in each case, in the form filed or required to be filed with the Commission or, if not required to be filed, in the form retained in the Company’s records pursuant to Rule 433(g), is herein called the “Prospectus.”

Any reference herein to the Registration Statement, the Prospectus Supplement, the Prospectus or any issuer free writing prospectus shall be deemed to refer to and include the documents, if any, that are or are deemed to be incorporated by reference therein (the “Incorporated Documents”), including, unless the context otherwise requires, the documents, if any, filed as exhibits to such Incorporated Documents. Any reference herein to the terms “amend,” “amendment” or “supplement” with respect to the Registration Statement, the Prospectus Supplement, the Prospectus or any issuer free writing prospectus shall be deemed to refer to and include the filing of any document under the Exchange Act on or after the most recent effective date of the Registration Statement, or the respective dates of the Prospectus Supplement, Prospectus or such issuer free writing prospectus, as the case may be, and incorporated therein by reference. For purposes of this Agreement, all references to the Registration Statement, the Prospectus or any amendment or supplement thereto shall be deemed to include the most recent copy filed with the Commission pursuant to its Electronic Data Gathering Analysis and Retrieval System or, if applicable, the Interactive Data Electronic Application system when used by the Commission (collectively, “EDGAR”).”

3.                   Delivery of Placement Shares. Section 5(b) of the Agreement is hereby amended and restated in its entirety to read as follows:

“On or before each Settlement Date, the Company will issue the Placement Shares being sold on such date and will, or will cause its transfer agent to, electronically transfer such Placement Shares by crediting the Agent’s or its designee’s account (provided the Agent shall have given the Company written notice of such designee prior to the Settlement Date) at The Depository Trust Company through its Deposit and Withdrawal at Custodian System (“DWAC”) or by such other means of delivery as may be mutually agreed upon by the parties hereto, which in all cases shall be duly authorized, freely tradeable, transferable, registered shares of Common Stock in good deliverable form. On each Settlement Date, the Agent will deliver the related Net Proceeds in same day funds to an account designated by the Company on or prior to the Settlement Date. The Agent shall be responsible for providing DWAC instructions or other instructions for delivery by other means with regard to the transfer of the Placement Shares being sold. In addition to and in no way limiting the rights and obligations set forth in Section 9(a) hereto, the Company agrees that if the Company or its transfer agent (if applicable), defaults in its obligation to deliver duly authorized, freely tradeable, transferable, registered Placement Shares in good deliverable form by 2:30 P.M., New York City time, on a Settlement Date (or such later time that is three (3) hours following the Agent’s delivery of instructions for delivery Placement Shares by notification of the Company’s transfer agent that the DWAC request has been initiated and provided further that no such default shall be deemed to occur if it is the result of a failure by the Agent to provide instructions for delivery of the Placement Shares), the Company will (i) take all necessary action to cause the full amount of any Net Proceeds that were delivered to the Company’s account with respect to such settlement, together with any costs incurred by the Agent and/or its clearing firm in connection with recovering such Net Proceeds, to be immediately returned to the Agent or its clearing firm no later than 5:00 P.M., New York City time, on such Settlement Date, by wire transfer of immediately available funds to an account designated by the Agent or its clearing firm, (ii) indemnify and hold the Agent and its clearing firm harmless against any loss, claim, damage, or expense (including reasonable legal fees and expenses), as incurred, arising out of or in connection with such default by the Company or its transfer agent (if applicable) and (iii) pay to the Agent any commission, discount or other compensation to which it would otherwise have been entitled absent such default. Certificates for the Placement Shares, if any, shall be in such denominations and registered in such names as the Agent may request in writing one Business Day (as defined below) before the applicable Settlement Date. Certificates for the Placement Shares, if any, will be made available by the Company for examination and packaging by the Agent in New York City not later than 12:00 P.M., New York City time, on the Business Day prior to the applicable Settlement Date.”

4.                   Expenses. Section 7(g) is hereby amended by adding the following sentence to the end of the Section:

“The Company will not be responsible for the payment of any incremental expenses resulting from the Agent’s failure to cause timely settlement of each sale of Placement Shares on the applicable Settlement Date to the extent such failure is caused by the Agent’s delay or failure: (i) to provide instructions for delivery of the Placement Shares or (ii) to complete the settlement of the sale of Placement Shares following receipt of such Placement Shares from the Company’s transfer agent.”

5.                   Notices. Section 12 is hereby amended and restated in its entirety to read as follows: 

All notices or other communications required or permitted to be given by any party to any other party pursuant to the terms of this Agreement shall be in writing, unless otherwise specified in this Agreement, and if sent to the Agent, shall be delivered to:

Chardan Capital Markets, LLC

One Pennsylvania Plaza, Suite 4800

New York, New York 10119

Attention: Shai Gerson

E-mail: sgerson@chardan.com

with a copy (which shall not constitute notice) to:

Goodwin Procter LLP

The New York Times Building

620 Eighth Avenue

New York, New York 10018

Attention: Justin S. Platt

E-mail: jplatt@goodwinlaw.com

and if to the Company, shall be delivered to:

Hyperion DeFi, Inc.

23461 South Pointe Drive, Suite 390

Laguna Hills, California 92653

Attention: Interim Chief Executive Officer

E-mail: hyunsu@hyperiondefi.com

with a copy (which shall not constitute notice) to:

Covington & Burling LLP

One International Place

Suite 1020

Boston, Massachusetts 02110

Attention: Megan Gates

E-mail: MGates@cov.com

6.                   Governing Law. THIS AMENDMENT AND ANY CLAIM, CONTROVERSY OR DISPUTE ARISING UNDER OR RELATED TO THIS AMENDMENT SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK, WITHOUT REGARD TO THE PRINCIPLES OF CONFLICTS OF LAWS.

7.                    Counterparts. This Amendment may be executed in two or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument. Delivery of an executed Agreement by one party to the other may be made by facsimile or electronic transmission. Counterparts may be delivered via facsimile, electronic mail (including any electronic signature covered by the U.S. federal ESIGN Act of 2000, Uniform Electronic Transactions Act, the Electronic Signatures and Records Act or other applicable law, e.g., www.docusign.com) or other transmission method and any counterpart so delivered shall be deemed to have been duly and validly delivered and be valid and effective for all purposes.

8.                   Agreement Remains in Effect. Except as provided herein, all provisions, terms and conditions of the Agreement shall remain in full force and effect. As amended hereby, the Agreement is ratified and confirmed in all respects.

Terms used herein but not otherwise defined are used herein as defined in the Agreement.

(Signature page follows)  

If the foregoing correctly sets forth the understanding between the Company and the Agent, please so indicate in the space provided below for that purpose, whereupon this letter shall constitute a binding agreement between the Company and the Agent.

Exhibit 5.1

September 24, 2025

Hyperion DeFi, Inc.

23461 South Pointe Drive, Suite 390

Laguna Hills, CA 92653

Ladies and Gentlemen:

We have acted as counsel to Hyperion DeFi, Inc. (f/k/a Eyenovia, Inc.), a Delaware corporation (the “Company”), in connection with the issuance and sale of additional shares of the Company’s common stock, par value $0.0001 per share (the “Common Stock”), having an aggregate offering price of up to $60,225,987 (the “Shares”), pursuant to the Amended and Restated Sales Agreement, dated December 30, 2024, as amended by Amendment No. 1, dated September 24, 2025 (as amended, the “Sales Agreement”) between the Company and Chardan Capital Markets, LLC, as sales agent. The offer and sale of the Shares are being registered under the Securities Act of 1933 (the “Securities Act”) pursuant to the Company’s registration statement on Form S-3 (File No. 333-282458), which was filed with the Securities and Exchange Commission (the “SEC”) on October 1, 2024 (the “Registration Statement”).

We have reviewed the Sales Agreement, the Registration Statement and the prospectus, dated October 8, 2024, as supplemented by a prospectus supplement with respect to the offer and sale of the Shares, as filed with the SEC on December 30, 2024 and as further supplemented on the date hereof. We have also reviewed the notice of the Registration Statement’s effectiveness, dated October 8, 2024, posted on the website of the SEC at www.sec.gov, and such other corporate records, certificates and other documents, and such questions of law, as we have considered necessary or appropriate for the purposes of this opinion.

We have assumed that (i) all signatures are genuine, that all documents submitted to us as originals are authentic and that all copies of documents submitted to us conform to the originals, and (ii) upon the issuance of any of the Shares, the total number of shares of Common Stock issued and outstanding will not exceed the total number of shares of Common Stock that the Company is then authorized to issue under its certificate of incorporation, as amended and restated from time to time.

We have relied as to certain matters on information obtained from public officials, officers of the Company and other sources believed by us to be responsible.

Based upon the foregoing, we are of the opinion that the Shares have been duly authorized, and when issued and sold by the Company pursuant to the terms of the Sales Agreement and upon receipt by the Company of full payment therefor in accordance with the Sales Agreement, will be validly issued, fully paid and non-assessable.

We are members of the bar of the Commonwealth of Massachusetts. We do not express any opinion herein on any laws other than the Delaware General Corporation Law.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Company’s Current Report on Form 8-K dated the date hereof related to the offering of the Shares. We also hereby consent to the reference to our firm under the heading “Legal Matters” in the prospectus supplement constituting part of the Registration Statement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.